The Effect of Air Pressure on the Buoyancy of an Eye Dropper
Thendral, Avi, and Walter
Introduction
In this experiment, we tested the effect of air pressure in the vacuum and the amount of water in the eye dropper on the buoyancy of the eye dropper. Archimedes already worked on buoyancy, and his principle states that the buoyancy force on a floating object is equal to the mass of the volume of water displaced by that object multiplied by its gravitational acceleration. Also, the pressure produced when a material of lower density gets to height h of higher density p,
All of the forces pushing on a system are equal (the system is in equilibrium) if
where Fsubi is the applied forece and sigma rsubi is the virtual displacement.
If a cylinder is partially submerged in a liquid, and the area of the cylinder's base is A, the length is l, and the density is p, the density of the fluid is psub0, the depth of the submerged cylinder is x, and the depth the cylinder is submerged at equilibrium is xsub0,
We did an experiment to find out how the amount of water in the eye dropper affects how many kiloPascals of pressure it takes to make the dropper float. We hypothesized that the less water there is in the eye dropper, the lower the air pressure that the dropper needs to move up. We also found out how the amount of water in the eye dropper affects how long it takes to go up. We were not even sure that the amount of water in the eye dropper affects the time the dropper takes to get to the top.
Procedure
We started with a glass eye dropper with a copper wire wrapped around it. The empty eye dropper weighed 5.77 grams. We measured the volume of the eye dropper by estimating half of the eye dropper. Then we filled up the dropper half way, poured it into a glass vial with milliliter markings, and repeated that step again. We estimated the volume of the glass part of the eye dropper to be about 1.6mL. Since part of the cap was going to be either empty or filled with water, we estimated the volume of that. We estimated how much of the cap was going to be part of the volume, and we filled that much of the cap up with water. Then we poured that water into the vial with milliliter markings, and it was 1.25mL. Finally, we added the volume of the glass eye dropper by itself to the volume of the cap and got 2.85mL for the estimated volume of the whole thing.
To begin with, we filled up the eye dropper to .25mL in a 100mL vial that was filled up to 90mL with 2.7cm diameter. We put the vial and the dropper in a vacuum pump, and started pumping the air out. We recorded how many kiloPascals of pressure there were in the vacuum when the eye dropper began to move up. We repeated this three times. Then we repeated the same steps with .5mL of water in the eye dropper, then with .75mL, and finally with 1mL in the eye dropper.
Next, we put the vial with the eye dropper that was .25mL full in the vacuum pump, pumped out the air until the pressure in the vacuum was the pressure at which the dropper started moving, and measured the time it took for the dropper to move to the top of the 100mL vial filled up to 90mL. We timed the movement of the eye dropper by starting the stopwatch when the dropper started moving up and stopping the watch when it reached the top. The dropper had to travel 11.3cm to get to the top. We measured the time it took for the dropper that was .25mL full to move to the top of the vial twice. Then we repeated the same steps with .5mL of water in the eye dropper, then with .75mL, and finally we did it with 1mL of water in the eye dropper
Results
In the first test, which looked at the the air pressure at which the dropper started to move up, we found a linear trend. As the amount of water in the dropper increased, the air pressure at which the dropper started moving up decreased by about 2 KiloPascals.
mL kiloPascals
0.25 100.5
0.25 98
0.25 100
0.50 96
0.50 97
0.50 97.2
0.75 94
0.75 94
0.75 95.2
1.00 91.5
1.00 92
1.00 92.2
The p-value when comparing .25 mL and .5mL is .0497, .0130 when comparing .5 mL and .75 mL, and .0115 when comparing .75 mL and 1.0 mL.
For the second test, we looked at the time the dropper took to reach the top once it had started moving. For this test, we found no significant correlation between the amount of water in the eye dropper and the time the dropper took to reach the top.
We found that in the first test, the more water inside the eye dropper correlated with lower values of air pressure at which the eye dropper started moving upwards. This disproved our hypothesis. The low p-values confirm that there is a significant difference in the amount of air pressure needed to move an eye dropper up with different amounts of water. For the second test, no conclusions can be made until more trials are conducted. To improve the accuracy of the second test, researchers should use a longer tube to create a longer distance the dropper covers over an amount of time. We also noticed that after conducting a few trials inside the vacuum, the water inside the vial was noticeably warmer, which could be a possible source for error, resulting in an unaccounted for variable.
Table of Contents
The Effect of Air Pressure on the Buoyancy of an Eye Dropper
Thendral, Avi, and WalterIntroduction
In this experiment, we tested the effect of air pressure in the vacuum and the amount of water in the eye dropper on the buoyancy of the eye dropper. Archimedes already worked on buoyancy, and his principle states that the buoyancy force on a floating object is equal to the mass of the volume of water displaced by that object multiplied by its gravitational acceleration. Also, the pressure produced when a material of lower density gets to height h of higher density p,All of the forces pushing on a system are equal (the system is in equilibrium) if
where Fsubi is the applied forece and sigma rsubi is the virtual displacement.
If a cylinder is partially submerged in a liquid, and the area of the cylinder's base is A, the length is l, and the density is p, the density of the fluid is psub0, the depth of the submerged cylinder is x, and the depth the cylinder is submerged at equilibrium is xsub0,
We did an experiment to find out how the amount of water in the eye dropper affects how many kiloPascals of pressure it takes to make the dropper float. We hypothesized that the less water there is in the eye dropper, the lower the air pressure that the dropper needs to move up. We also found out how the amount of water in the eye dropper affects how long it takes to go up. We were not even sure that the amount of water in the eye dropper affects the time the dropper takes to get to the top.
Procedure
We started with a glass eye dropper with a copper wire wrapped around it. The empty eye dropper weighed 5.77 grams. We measured the volume of the eye dropper by estimating half of the eye dropper. Then we filled up the dropper half way, poured it into a glass vial with milliliter markings, and repeated that step again. We estimated the volume of the glass part of the eye dropper to be about 1.6mL. Since part of the cap was going to be either empty or filled with water, we estimated the volume of that. We estimated how much of the cap was going to be part of the volume, and we filled that much of the cap up with water. Then we poured that water into the vial with milliliter markings, and it was 1.25mL. Finally, we added the volume of the glass eye dropper by itself to the volume of the cap and got 2.85mL for the estimated volume of the whole thing.
To begin with, we filled up the eye dropper to .25mL in a 100mL vial that was filled up to 90mL with 2.7cm diameter. We put the vial and the dropper in a vacuum pump, and started pumping the air out. We recorded how many kiloPascals of pressure there were in the vacuum when the eye dropper began to move up. We repeated this three times. Then we repeated the same steps with .5mL of water in the eye dropper, then with .75mL, and finally with 1mL in the eye dropper.Next, we put the vial with the eye dropper that was .25mL full in the vacuum pump, pumped out the air until the pressure in the vacuum was the pressure at which the dropper started moving, and measured the time it took for the dropper to move to the top of the 100mL vial filled up to 90mL. We timed the movement of the eye dropper by starting the stopwatch when the dropper started moving up and stopping the watch when it reached the top. The dropper had to travel 11.3cm to get to the top. We measured the time it took for the dropper that was .25mL full to move to the top of the vial twice. Then we repeated the same steps with .5mL of water in the eye dropper, then with .75mL, and finally we did it with 1mL of water in the eye dropper
Results
In the first test, which looked at the the air pressure at which the dropper started to move up, we found a linear trend. As the amount of water in the dropper increased, the air pressure at which the dropper started moving up decreased by about 2 KiloPascals.mL kiloPascals
0.25 100.5
0.25 98
0.25 100
0.50 96
0.50 97
0.50 97.2
0.75 94
0.75 94
0.75 95.2
1.00 91.5
1.00 92
1.00 92.2
The p-value when comparing .25 mL and .5mL is .0497, .0130 when comparing .5 mL and .75 mL, and .0115 when comparing .75 mL and 1.0 mL.
For the second test, we looked at the time the dropper took to reach the top once it had started moving. For this test, we found no significant correlation between the amount of water in the eye dropper and the time the dropper took to reach the top.
mL kiloPascals
0.25 1.9
0.25 2.1
0.50 1.8
0.50 2.7
0.75 2.3
0.75 2.5
1.00 2.4
1.00 2
Conclusions
We found that in the first test, the more water inside the eye dropper correlated with lower values of air pressure at which the eye dropper started moving upwards. This disproved our hypothesis. The low p-values confirm that there is a significant difference in the amount of air pressure needed to move an eye dropper up with different amounts of water. For the second test, no conclusions can be made until more trials are conducted. To improve the accuracy of the second test, researchers should use a longer tube to create a longer distance the dropper covers over an amount of time. We also noticed that after conducting a few trials inside the vacuum, the water inside the vial was noticeably warmer, which could be a possible source for error, resulting in an unaccounted for variable.References
Weisstein, Eric W. Buoyancy Force.
Weisstein, Eric W. Buoyancy Pressure.
Weisstein, Eric W. Mechanical Equilibrium.
Weisstein, Eric W. Buoyancy Oscillation.